directional hypothesis

make a prediction regarding direction i.e. increase...or decrease...

one-tail test

non-directional hypothesis

no prediction regarding direction- just know there is a change, don't know in/decrease

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two-tail test

need to look/think about both extremes- 5% > 1.96- 1% > 2.57

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distribution of means

set of sample means from a given population

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rule #1

the mean of a distribution of means (μm) is the same as the mean of the population of individuals

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rule #2a

The variance of the distribution of means is the variance of the population of individuals divided by the number of individuals in each sample

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rule #2b

the standard deviation of the distribution of means is the square root of the variance of the distribution of means

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rule #3

the shape of the distribution of means is approximately normal if at least one of the conditions is met- sample size is 30 or more- the distribution of the population of individual scores is normally distributed

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Variance & SD formulas for Distribution of Means

variance --> δ²m = δ² / NSD --> √δ²m = δ² / N or √δ²m

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z-test

hypothesis testing procedure using the mean of the sample when the population variance is known- comparing sample mean to distribution of means

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z-test formula

Z = (M - μm) / δ²

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statistical significance

the number is so extreme it is unlikely to have gotten it by chance

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Alpha (α) - Type I Error

- the null is true and the data tells us to rejecti.e. jury finding innocent man guilty

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Beta (β) - Type II Error

- the null is false and the data tells us to retain iti.e. jury lets guilty man go free

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comparing studies

- as long as you have statistical significance, neither score is more than the other

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practical significance

difference meaningful in real-world context- one leads to more improvement over other

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effect sizes

the extent to which population means differ and distributions overlap

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large effect size

little overlap with vastly different means

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small effect size

a lot of overlap with different but close means

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Cohen's D

measure of effect size- mean and how spread out the distribution is (SD/SE)- allows us to examine practical significance (how different the groups are) and compare studies

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effect size cut-offs

small = .2medium = .5large = .8

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statistical power

the probability that a study will yield a statistically significant result if the research hypothesis is really true- opposite is beta/type II error